Check the pins in the electrical connectors. A long time ago a friend had a boat where the motor would suddenly cut out at full throttle. Eventually it was discovered that one of the pins in the connector from the remote control box was not fully pushed into place. At high rpms the vibration of the engine would cause the connection to be intermittent. To the engine it would seem as if someone turned the ignition switch off.

A bit of foil stuffed into the corresponding female pin solved the problem.

How old is that engine ? Used to have a 96 Evi 15 HP with same sypmtons, removed cylinder head, cleaned all internal crankcase and head water passages, placed a new well torqued head gasket + new spark plugs and bingo!! Still runing up to date.

Head gaskets are not eternal, with time and use they compress and hardens, when engine is hot lets small water particles pass into combustion chambers causing strange symptoms at speeds higher than idle, worsens between 3/4 to wot and even can shut engine down.

Nobody retorques head gasket when engine has passed break in period because a torque wrench is needed, this causes premature gasket wear due to salt water penetration & corrosion between crankcase and head walls losing perfect chamber seal as when engine was brand new.

If all related fuel, electrical, mechanical is working ok this is the inmediate part to check and change. Remenber outboards are not car that uses glycol for engine refrigeration. To get the idea...

Just an idea,
Your fouling of the prop will have created a mess. All sorts of vacuum issues with stalling and sucking shit it under higher pressure than it should be. You'll be hoovering up all sorts of shit from plenums, fuels bowls etc., esp. if it's a forced stall and not an powerhead one (fuel starvation or electro).
Probably has been said but I read the first and last page only, having experienced this myself ( professionally and on hols ), I'd clean out all your fuel reservoirs. Floats, filters and tanks. It only takes one paint flake to hide and cause hell Taliban style and you're mullered.